Alternative symplectic structures for SO(3,1) and SO(4) four-dimensional BF theories

The most general action, quadratic in the B fields as well as in the curvature F, having SO(3,1) or SO(4) as the internal gauge group for a four-dimensional BF theory is presented and its symplectic geometry is displayed. It is shown that the space of solutions to the equations of motion for the BF theory can be endowed with symplectic structures alternative to the usual one. The analysis also includes topological terms and cosmological constant. The implications of this fact for gravity are briefly discussed.Comment: 13 pages, LaTeX file, no figure

Feedback-limited Accretion: Luminous Signatures from Growing Planets

Planets form in discs of gas and dust around stars, and keep growing by accretion of disc material while available. Massive planets clear a gap in that protoplanetary disc, but still accrete through spiral wakes. On its way to the planet, the gas will settle on a \emph{circumplanetary} disc around the planet and slowly accrete on to it. The energy of the accreted gas will be released, heating the planet surroundings in a feedback process. For high enough accretion rates the planet should be detectable at infrared wavelengths. We aim to find whether detectable planet luminosities, $\gtrsim 10^{-3} \, \textrm{L}_\odot$, can occur when considering that the planet luminosity is coupled to the accretion, and also to study which other effects has the feedback on the dynamics of the circumplanetary and the gap regions. We model a planet with mass ratio $q=10^{-3}$, orbiting at 10 AU from a solar mass star, using a modified version of the 2D code FARGO-AD, which includes a prescription for the accretion and feedback luminosity of the planet. We find that the planetary feedback is able to partially deplete the circumplanetary disc, and to reduce the accretion rate onto the planet. However, detectable luminosities of $L_\textrm{p}\gtrsim 10^{-3}\, \textrm{L}_\odot$ are still produced. The feedback also contributes to partially refilling the gap, to heat up the coorbital region, and to perturb the orbital velocity of the gas.Comment: Submitted to MNRA

Lorentz-covariant Hamiltonian analysis of BF gravity with the Immirzi parameter

We perform the Lorentz-covariant Hamiltonian analysis of two Lagrangian action principles that describe general relativity as a constrained BF theory and that include the Immirzi parameter. The relation between these two Lagrangian actions has been already studied through a map among the fields involved. The main difference between these is the way the Immirzi parameter is included, since in one of them the Immirzi parameter is included explicitly in the BF terms, whereas in the other (the CMPR action) it is in the constraint on the B fields. In this work we continue the analysis of their relationship but at the Hamiltonian level. Particularly, we are interested in seeing how the above difference appears in the constraint structure of both action principles. We find that they both possess the same number of first-class and second-class constraints and satisfy a very similar (off-shell) Poisson-bracket algebra on account of the type of canonical variables employed. The two algebras can be transformed into each other by making a suitable change of variablesComment: LaTeX file, no figure

Linear constraints from generally covariant systems with quadratic constraints

How to make compatible both boundary and gauge conditions for generally covariant theories using the gauge symmetry generated by first class constraints is studied. This approach employs finite gauge transformations in contrast with previous works which use infinitesimal ones. Two kinds of variational principles are taken into account; the first one features non-gauge-invariant actions whereas the second includes fully gauge-invariant actions. Furthermore, it is shown that it is possible to rewrite fully gauge-invariant actions featuring first class constraints quadratic in the momenta into first class constraints linear in the momenta (and homogeneous in some cases) due to the full gauge invariance of their actions. This shows that the gauge symmetry present in generally covariant theories having first class constraints quadratic in the momenta is not of a different kind with respect to the one of theories with first class constraints linear in the momenta if fully gauge-invariant actions are taken into account for the former theories. These ideas are implemented for the parametrized relativistic free particle, parametrized harmonic oscillator, and the SL(2,R) model.Comment: Latex file, revtex4, 18 pages, no figures. This version includes the corrections to many misprints of v1 and also the ones of the published version. The conceptual and technical parts of the paper are not altere

Real sector of the nonminimally coupled scalar field to self-dual gravity

A scalar field nonminimally coupled to gravity is studied in the canonical framework, using self-dual variables. The corresponding constraints are first class and polynomial. To identify the real sector of the theory, reality conditions are implemented as second class constraints, leading to three real configurational degrees of freedom per space point. Nevertheless, this realization makes non-polynomial some of the constraints. The original complex symplectic structure reduces to the expected real one, by using the appropriate Dirac brackets. For the sake of preserving the simplicity of the constraints, an alternative method preventing the use of Dirac brackets, is discussed. It consists of converting all second class constraints into first class by adding extra variables. This strategy is implemented for the pure gravity case.Comment: Latex file, 22 pages, no figure

Relational evolution of the degrees of freedom of generally covariant quantum theories

We study the classical and quantum dynamics of generally covariant theories with vanishing a Hamiltonian and with a finite number of degrees of freedom. In particular, the geometric meaning of the full solution of the relational evolution of the degrees of freedom is displayed, which means the determination of the total number of evolving constants of motion required. Also a method to find evolving constants is proposed. The generalized Heinsenberg picture needs M time variables, as opposed to the Heisenberg picture of standard quantum mechanics where one time variable t is enough. As an application, we study the parameterized harmonic oscillator and the SL(2,R) model with one physical degree of freedom that mimics the constraint structure of general relativity where a Schrodinger equation emerges in its quantum dynamics.Comment: 25 pages, no figures, Latex file. Revised versio

Estimating Venezuelas Latent Inflation

Percent variation of the consumer price index (CPI) is the inflation indicator most widely used. This indicator, however, has some drawbacks. In addition to measurement errors of the CPI, there is a problem of incongruence between the definition of inflation as a sustained and generalized increase of prices and the traditional measure associated with the CPI. We use data from 1991 to 2005 to estimate a complementary indicator for Venezuela, the highest inflation country in Latin America. Latent inflation is defined as that component of measured inflation that has no impact on real output in the long-run. This notion, consequently, is consistent with a vertical long-run Phillips curve and therefore it is grounded on economic theory. Latent inflation is constructed placing dynamic restrictions on a structural vector auto regression system. We find that latent inflation reflects more closely the generalized and sustained price increases most likely to be impacted by monetary policy. Our results are consistent with the identifying restrictions and with the theoretical definition of inflation